OFFSET
1,1
COMMENTS
Eggleton and MacDougall show that there are no more than 419 terms in this sequence. - T. D. Noe, Oct 13 2008
a(24) > 10^13. - Donovan Johnson, Jan 15 2009
LINKS
Donovan Johnson, Table of n, a(n) for n = 1..23
Roger B. Eggleton and James A. MacDougall, Consecutive integers with equally many principal divisors, Math. Mag. 81 (2008), 235-248.
EXAMPLE
a(6) = a(7) = 1217250 because the relevant 7 successive numbers have 4 distinct prime factors:
1217250 = 2 * 3^2 * 5^3 * 541;
1217251 = 7 * 17 * 53 * 193;
1217252 = 2^2 * 23 * 101 * 131;
1217253 = 3 * 47 * 89 * 97;
1217254 = 2 * 19 * 103 * 311;
1217255 = 5 * 13 * 61 * 307;
1217256 = 2^3 * 3 * 67 * 757.
MATHEMATICA
k=1; Do[While[Union[Table[Length[FactorInteger[i]], {i, k, k+n-1}]]!={4}, k++ ]; Print[k], {n, 1, 8}]
Module[{d4=Table[If[PrimeNu[n]==4, 1, 0], {n, 143*10^5}]}, Flatten[Table[ SequencePosition[d4, PadRight[{}, n, 1], 1], {n, 8}], 1][[All, 1]]] (* Requires Mathematica version 10 or later *) (* This generates the first 8 terms of the sequence *) (* Harvey P. Dale, Aug 25 2017 *)
CROSSREFS
KEYWORD
nonn,fini
AUTHOR
Labos Elemer, Sep 26 2003
EXTENSIONS
More terms from Don Reble, Sep 29 2003
a(13)-a(19) from Donovan Johnson, Mar 06 2008
a(20)-a(23) from Donovan Johnson, Jan 15 2009
STATUS
approved